Pinchoff and satellite formation in compound viscous threads

Abstract

The breakup of viscous compound threads in the presence of insoluble surfactant at both interfaces is investigated. We use asymptotic methods in the limit of long axisymmetric waves to derive a coupled system of five one-dimensional (1-D) partial differential equations governing the evolution of the outer and inner interfaces, the surfactant concentrations there, and the leading order axial velocity component in the jet. The linear, and nonlinear, stability of these equations is then investigated for a wide range of outer to inner viscosity ratio, m, outer to inner surface tension ratio, γ, the ratio of initial outer to inner radii, α, initial surfactant concentrations at the outer and inner interfaces, Γ10 and Γ20, surfactant activities, β1 and β2, and the Schmidt numbers, Sc1 and Sc2, defined as the ratio of the kinematic viscosity to the surfactant surface diffusion coefficient. We also show that if Sc1 = Sc2, these results are recovered via solution of 1-D evolution equations governing the dynamics of an effective single surfactant covered thread, which are obtained through appropriate rescalings; these rescalings are detailed herein. © 2003 American Institute of Physics.